My $HOME\_vimrc does not have this option. I was led to believe that Vim first invokes the system _vimrc in $VIM, then moves on to the user _vimrc in their respective $HOMEs, but it's obvious here that that's no longer the case here. This is important because I need to move all of my personal configs somewhere else, and $VIM is not a good option. Any help would be appreciated.

Edit 1

After the use of :scriptnames as per recommendations of the comment below, I found that indeed, a) $VIM\_vimrc was not used, and b) the first file used was $HOME\_vimrc. I need Vim to use, first and foremost, $VIM\_vimrc, so that Vim recognizes $HOME to be elsewhere of the C:\Users\foo that I currently use.

No, it's still not correct, $VIM/vimrc is always read. Then the first one of $HOME/_vimrc, $HOME/vimfiles/vimrc, or $VIM/_vimrc (this time with a leading underscore) is read. Vim also accepts a leading dot instead of an underscore. Note that you can have both $VIM/vimrc and $VIM/_vimrc, the first one as a system wide initialization file and the second one as a user initialization file which is ignored if $HOME/_vimrc exists. When you look at :help vimrc, steps a. to d. define the order of initialization. The part about the vimrc files before step a. is just informative.
– Jürgen KrämerAug 13 at 13:41

Oh, I probably didn't have $VIM/vimrc in the first place, that's why it wasn't on :scriptnames. Thanks!
– Paul KimAug 13 at 13:43